Respuesta :
Given the Radical Equation:
[tex]\sqrt{3t+5}=8[/tex]• You can solve it as follows:
1. Square both sides of the equation in order to undo the effect of the square root, because, by definition:
[tex](\sqrt[]{b})^2=b[/tex]Then:
[tex]\begin{gathered} (\sqrt{3t+5})=(8)^2 \\ \\ 3t+5=64 \end{gathered}[/tex]2. Apply the Subtraction Property of Equality by subtracting 5 from both sides of the equation:
[tex]\begin{gathered} 3t+5-(5)=64-(5) \\ \\ 3t=59 \end{gathered}[/tex]3. Apply the Division Property of Equality by dividing both sides of the equation by 3:
[tex]\begin{gathered} \frac{3t}{3}=\frac{59}{3} \\ \\ t=\frac{59}{3} \end{gathered}[/tex]• In order to check the solution, you need to substitute it into the original equation and evaluate it. If both sides of the equation are equal, then the equation is true:
[tex]\sqrt[]{3(\frac{59}{3})+5}=8[/tex][tex]\sqrt[]{\frac{59\cdot3}{3}+5}=8[/tex][tex]\sqrt[]{59+5}=8[/tex][tex]\begin{gathered} \sqrt[]{64}=8 \\ \\ 8=8\text{ (True)} \end{gathered}[/tex]Hence, the answer is:
[tex]\text{Solution: }t=\frac{59}{3}[/tex]